Here's something you should know: solid deodorant/antiperspirant sticks are not liquids and do not need to fit in your zip bag. The only time that you need to put deodorant/antiperspirant into the 3qt baggie is if you use a liquid form (these typically roll on). You should never have a reason to need to purchase a travel size deodorant/antiperspirant stick; just toss it somewhere else in your bag and make some room for the things that are actual liquid.
PS -- once you clear security, toss your 3qt bag into a one gallon, heavy-duty freezer bag; I've seen 3qt bags fail in containing sandwiches and I definitely don't need it failing while containing spilled liquids.
Picture from bosconet